Characteristics of breaking irregular wave forces on a monopile

The substructures of offshore wind turbines are subjected to extreme breaking irregular wave forces. The present study is focused on investigating breaking irregular wave forces on a monopile using a computational fluid dynamics (CFD) based numerical model. The breaking irregular wave forces on a monopile mounted on a slope are investigated with a numerical wave tank. The experimental and numerical irregular free surface elevations are compared in the frequency-domain for the different locations in the vicinity of the cylinder. A numerical analysis is performed for different wave steepness cases to understand the influence of wave steepness on the breaking irregular wave loads. The wave height transformation and energy level evolution during the wave shoaling and wave breaking processes is investigated. The higher-frequency components generated during the wave breaking process are observed to play a significant role in initiating the secondary force peaks. The free surface elevation skewness and spectral bandwidth during the wave transformation process are analysed and an investigation is performed to establish a correlation of these parameters with the breaking irregular wave forces. The role of the horizontal wave-induced water particle velocity at the free surface and free surface pressure in determining the breaking wave loads is highlighted. The higher-frequency components in the velocity and pressure spectrum are observed to be significant in influencing the secondary peaks in the breaking wave force spectrum.     

An experimental investigation of plunging breaker boundary layers in the transformation zone

Experimental investigation is made on the boundary layers of the transformation zone (i.e. the region between the last symmetrical wave profile depth and the breaking point) of plunging breakers propagating on a smooth beach with 1/12 uniform slope. Using a laser anemometer, the particle velocities are measured at four verticals along the transformation zone for three different steepnesses of waves within the plunging breaker range. The boundary layer flow in the transformation zone is found mostly of turbulent character and vertical distribution of particle velocities does not seem to conform to the classical law of the wall distribution given for steady-flow boundary layers. The results show that free-stream particle velocities, in the boundary layer of the breaker under the crest phase, increase considerably as the wave progresses towards the breaking point. The boundary layer thickness, defined as the velocity-affected region, remains constant throughout the transformation zone but it decreases with increasing deep-water wave steepness for the particular beach slope tested.     

Characteristics of the Function of Ice Force on Vertical Cylindrical Piles

A lot of tests on ice forces on vertical cylindrical piles are conducted in the ice basin of ice laboratory in Tianjin University to identify the characteristics of ice forces on fixed platforms in the Bohai Gulf. A function of ice forces is simplified on basis of test data, and the charateristics of the ice forces including the amplitude of the force and the breaking frequency of the ice sheet is detailed by use of the Fast-Fourier-Transform method. The results show that the ice breaking frequency presents a linear relationship with the ratio of ice moving velocity to ice thickness at low velocities. At high velocities, the frequency remains constant with the increase of the ratio of ice moving velocity to ice thickness. These conclusions are compared those published in literature.     

浅水破碎波对直立圆柱作用力的试验研究

分析了桩柱破波力的构成特性,认为破碎波与桩柱作用过程中在不完全绕流区将出现由于附连质量迅速变化引起的冲击力和柱前后波面高度差引起的附加压差力;影响破碎波对直立圆柱作用力的因素应该包括确定破波特性的水底坡度i、入射深水波陡H_0/L_0及代表圆柱对破波作用影响的相对柱径D/H_0。通过从i=1/100到1/15五种底坡上桩柱破波力的系统试验,探索了桩柱破波力的作用特性,归纳了计算桩柱破波力的经验公式。     

The FUNWAVE model application and its validation using laboratory data

In this paper, the performance of a well known and widespread Boussinesq model is evaluated for its ability to predict deep waters and shoaling zone velocity and elevation, comparing them with laboratory data. The model evaluation places emphasis on the parameters of the wave field that could be used for the prediction of coastal phenomena. It was found that the model proved its ability to predict regular wave velocity and elevation both in deep waters and shoaling zones right up to the breaking region. In contrast to previous works found in literature, the comparisons in this case are not limited to modelled and measured wave elevations, but also involve horizontal velocities. As a result, experimental and computed time series of wave elevations and horizontal velocities and their corresponding phase-averaged values are investigated along the wave channel, showing a good performance of the model.     

One-dimensional modelling of individual waves and wave-induced longshore currents in the surf zone

A probabilistic model ( -model) was developed to describe the propagation and transformation of individual waves (wave by wave approach). The individual waves shoal until an empirical criterion for breaking is satisfied. Wave height decay after breaking is modelled by using an energy dissipation method. Wave-induced set-up and set-down and breaking-associated longshore currents are also modelled. Laboratory and field data were used to calibrate and verify the model. The model was calibrated by adjusting the wave breaking coefficient (as a function of local wave steepness and bottom slope) to obtain optimum agreement between measured and computed wave height. Four tests carried out in the large Delta flume of Delft Hydraulics were considered. Generally, the measured H_1/3-wave heights are reasonably well represented by the model in all zones from deep water to the shallow surf zone. The fraction of breaking waves was reasonably well represented by the model in the upsloping zones of the bottom profile. Verification of the model results with respect to wave-induced longshore current velocities was not extensive, because of a lack of data. In case of a barred profile the measured longshore velocities showed a relatively uniform distribution in the (trough) zone between the bar crest and the shoreline, which could to some extent be modelled by including space-averaging of the radiation force gradient, horizontal mixing and longshore water surface gradients related to variations in set-up. In case of a monotonically upsloping profile the cross-shore distribution of the longshore current velocities is reasonably well represented.     

Laboratory study of wave and turbulence velocities in a broad-banded irregular wave surf zone

The characteristics of wave and turbulence velocities created by a broad-banded irregular wave train breaking on a 1:35 slope were studied in a laboratory wave flume. Water particle velocities were measured simultaneously with wave elevations at three cross-shore locations inside the surf zone. The measured data were separated into low-frequency and high-frequency time series using a Fourier filter. The measured velocities were further separated into organized wave-induced velocities and turbulent velocity fluctuations by ensemble averaging. The broad-banded irregular waves created a wide surf zone that was dominated by spilling type breakers. A wave-by-wave analysis was carried out to obtain the probability distributions of individual wave heights, wave periods, peak wave velocities, and wave-averaged turbulent kinetic energies and Reynolds stresses. The results showed that there was a consistent increase in the kurtosis of the vertical velocity distribution from the surface to the bottom. The abnormally large downward velocities were produced by plunging breakers that occurred from time to time. It was found that the mean of the highest one-third wave-averaged turbulent kinetic energy values in the irregular waves was about the same as the time-averaged turbulent kinetic energy in a regular wave with similar deep-water wave height to wavelength ratio. It was also found that the correlation coefficient of the Reynolds stress varied strongly with turbulence intensity. Good correlation between u′ and w′ was obtained when the turbulence intensity was high; the correlation coefficient was about 0.3–0.5. The Reynolds stress correlation coefficient decreased over a wave cycle, and with distance from the water surface. Under the irregular breaking waves, turbulent kinetic energy was transported downward and landward by turbulent velocity fluctuations and wave velocities, and upward and seaward by the undertow. The undertow in the irregular waves was similar in vertical structure but lower in magnitude than in regular waves, and the horizontal velocity profiles under the low-frequency waves were approximately uniform.     

波浪增减水的实用数学模型及其数值模拟

提出了一种模拟近岸区波浪增减水的实用数学模型.首先采用考虑波能损失的抛物型缓坡方程数值模拟波浪破碎引起的波浪复振幅变化,接着根据计算得到的波浪复振幅,采用一种新的辐射应力公式计算辐射应力分量,然后采用深度平均方程计算波浪破碎产生的增减水.采用该模型对规则波和不规则波破碎引起的增减水进行了数值模拟,数值模拟结果与实验结果吻合良好,表明该模型可有效模拟近岸区由于波浪破碎引起的增减水.     

Large-wave simulation of three-dimensional,cross-shore and oblique,spilling breaking on constant slope beach

In this work, the large-wave simulation (LWS) method is adapted for application in spilling wave breaking over a constant slope beach. According to LWS, large scales of velocities, pressure and free-surface elevation are numerically resolved, while the corresponding unresolved scale effects are taken into consideration by a subgrid scale (SGS) model for wave and eddy stresses. The model may be not fully applicable in very shallow water, close to the shoreline, where the unresolved, turbulent, free-surface oscillation is of the same order with the water depth. Time integration of the Euler equations is achieved by a two-stage fractional scheme, combined with a hybrid scheme for spatial discretization, consisting of finite difference and pseudospectral approximation methods. Model parameters are calibrated by comparison to available experimental data of free-surface elevation and velocities in the surf zone for cross-shore incoming waves. The action of the wave SGS stresses in the outer coastal and surf zones initiates breaking and generates appropriate vorticity, in the form of an eddy structure (surface roller), at the breaking wavefront. At incipient breaking, both advection and gravity contribute to the vorticity flux at the free surface, while only after the full development of the surface roller, the effect of advection becomes stronger. The SGS model is also utilized to simulate propagation, refraction and breaking of oblique incoming waves. The gradual breaking and dissipation of wave crestlines and the surface roller structure along the breaking wavefront are automatically captured without any empirical input, such as data for the roller shape or the wave propagation angle at breaking.     

Experimental study of the breaking limit of multi-directional random waves passing over an impermeable submerged breakwater

This study investigates experimentally the breaking wave height of multi-directional random waves passing over an impermeable submerged breakwater. Experiments have been conducted in a three-dimensional wave basin equipped with a multi-directional random wave generator. A special type of wave gauge has been newly devised to record the water surface elevations in the breaker zone as accurately as possible. The records are analyzed to estimate the location and limit of wave breaking. Comparisons have also been made with the results of regular waves. The influence of the incident wave conditions on the breaking wave height normalized by the breakwater dimensions has been investigated. Empirical formulae have been presented to estimate the breaking limit of multi-directional random waves based on the experimental records. The formulae have been tested and found to work well not only for multi-directional random waves, but for regular waves as well.     

An analytically derived whitecap coverage model

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Experimental study of three-dimensional breaking wave kinematics

Particle image velocimetry has been used to examine three-dimensional breaking wave kinematics. Two cases of wave breaking were studied. In the first case, the wave field contains a single frequency with a uniform angular spreading within a given range {{ — , .}}. The wave field of the second case consists of a number of frequencies with a uniform angular spreading applied to each frequency. In both cases, the waves are designed such that the wave energy is focused at a given point. The degree of angular spreading has been found to have great effects on the breaking characteristics and kinematics. Two types of breaker were observed, the first being plunging and the second being spilling. Increasing the angular spreading had the effect of making the velocities within the extreme waves larger. The ratio of the crest velocity to the breaking wave speed was approximately unity under both single and multiple frequency conditions, regardless of the angular spreading.     

微尺度滑动平均方法计算海浪谱奇阶矩的公式

Glazman提出了一种计算海浪谱高阶谱矩的微尺度平均方法,但是,他利用随机过程理论导出的计算偶阶矩的公式和参照偶阶矩结论定义的奇阶矩计算公式之间存在着内在的不一致性.本文在Glazman工作的基础上根据随机过程理论推导了“微尺度平均方法”计算奇阶谱矩的公式,纠正了他的错误.上述结论随即应用于讨论破碎对波面水质点水平速度分布的影响.通过破碎的加速度判据考虑了破碎对速度分布的限制,给出了未破碎波面上水质点水平速度的的统计分布的初步结果.该分布取决于谱宽度参数及白浪覆盖率的大小,当白浪覆盖率较大时明显偏离正态分布.     

Approach to Calculating Methods of Wave Breaking Depth and Height

- Engineers in coastal engineering have been paying much attention to the research subject on wave breaking. In this paper, previous research results on the calculating methods of wave breaking depth and height are enumerated, the laws of wave transformation before and after wave breaking are investigated, an adequate supposition is made, and the effect of beach slope, bed friction and breaking turbulence on wave breaking is considered. By applying the theory of wave energy dissipation rate and combining with proper formulas of solitary waves, a new calculating formula of wave breaking depth and height on the movable bed is derived and examined with the data from experimental pools of different sizes, and it is proved to be of practicability.     

Wave-induced Benthic Velocity Variations in Shallow Waters

Waves propagating from deep water into shallow coastal areas produce oscillatory currents near the sea bottom. The magnitude of these currents depend upon the period and amplitude of the incoming waves, and the dissipation mechanism such as wave breaking and bottom friction. Field experiments in a gently shoaling bay, i.e. Cleveland Bay, Northern Australia, showed that there is a broad band of water at around 6 m depth, where the benthic surge velocities are maximum. Both further inshore and offshore, the bottom velocities were less than at 6 m depth, contrary to the normal expectation that the velocities should increase as the water becomes shallower. A new and computationally efficient wave model was developed and was able to reproduce experimental results for waves above 50 cm wave height, but not for small waves (wave height about 30 cm). One implication of this higher band of benthic surge velocities may be to produce high water turbidities in this region. Turbidity data from Cleveland Bay is consistent with this hypothesis.     

Random wave runup and overtopping a steep sea wall: Shallow-water and Boussinesq modelling with generalised breaking and wall impact algorithms validated against laboratory and field measurements

A semi-implicit shallow-water and Boussinesq model has been developed to account for random wave breaking, impact and overtopping of steep sea walls including recurves. At a given time breaking is said to occur if the wave height to water depth ratio for each individual wave exceeds a critical value of 0.6 and the Boussinesq terms are simply switched off. The example is presented of waves breaking over an offshore reef and then ceasing to break as they propagate inshore into deeper water and finally break as they run up a slope. This is not possible with the conventional criterion of a single onset of breaking based on rate of change of surface elevation which was also found to be less effective generally. The runup distribution on the slope inshore of the reef was well predicted. The model is tested against field data for overtopping available for Anchorsholme, Blackpool and corresponding 1:15 scale wave flume tests. Reflection of breaking waves impacting a steep sea wall is represented as a partial reversal of momentum flux with an empirically defined coefficient. Offshore to nearshore significant wave height variation was reasonably predicted although nearshore model spectra showed distinct differences from the experiments. The breaking wave shape described by a shape parameter was also not well represented as might be expected for such a simple model. Overtopping agreement between model, field and flume was generally good although repeatability of two nominally identical flume experiments was only within 25%. Different distributions of random phase between spectral components can cause overall overtopping rates to differ by up to a factor of two. Predictions of mean discharge by EurOtop methods were within a factor of two of experimental measurements.     

关于波浪破碎特性的研究

有关波浪破碎问题的研究是海岸工程界十分关注的课题。本文列举了前人有关波浪破碎特性方面的研究成果；分析了波浪破碎前后波高的变化规律，作出了适当的假定；并考虑了动床海滩坡度、底摩擦以及紊动对波浪破碎特性的影响。应用波动能量耗散率理论，并结合孤立波理论的有关公式，作者推导了计算动床海滩上破碎指标ｒ_ｂ的公式，并进而给出破碎水深ｈ_ｂ与破碎波高Ｈ_ｂ的计算公式。通过不同规模实验水槽的资料验证表明，这组计算式具有广泛的实用性。     

Run-up of long waves on a beach: The influence of the incident wave form

The influence of the incident wave form on the extreme (maximal) characteristics of a wave at a beach (run-up and draw-down heights, run-up and draw-down velocities, and the breaking parameter) is studied. It is suggested to use in the calculations the definition of wavelength at a level of 2/3 of the maximal height, which to a certain degree correlates with the definition of the significant wavelength accepted in oceanology. Such a definition allows us to unify the relations for extreme run-up characteristics so that the influence of the incident wave form becomes insignificant. The obtained universal relations can be used for the estimates of run-up characteristics when the exact information about the form of the incident wave is not available.     

Wave forces on vertical cylinders upon shoals

An experimental study has been carried out on the forces from plunging breaking regular and irregular waves on a vertical cylinder on a shoal. Total as well as local wave forces have been measured. Engineering formulae for the calculation of the horizontal forces and overturning moments have been derived. The duration of the impact forces have been measured and compares fairly well with theoretical values.     

Violent breaking wave impacts. Part 1: Results from large-scale regular wave tests on vertical and sloping walls

As part of an investigation into the detailed characteristics of wave impacts, experimental data are presented for the impact pressures and forces generated by waves up to 1.7 m high breaking onto a vertical wall and a wall inclined at 27° to the vertical. Particular attention is given to the influence of entrained and entrapped air and, by selecting regular wave conditions that produce impacts, trends are identified for highly variable phenomena that could easily be missed when masked by the even greater variability associated with irregular waves.